Geometry

Chapter 5 Test

Points J, K, and L are the midpoints of the sides of ΔXYZ.

1. Find LK. 2. Find YK. 3. Find JK.

4. Algebra Find the value of x.

5. What is the distance across the lake?

6. Is it a shorter distance from A to B or from B to C? Explain.

7. What is the value of x?

8. Find AB.

9. Find BC.

10. is the perpendicular bisector of _____

11 Find MP.

12 Find NO.

13 Find NP.

Use the figure at the right.

14 Find the value of x.

15 Find mÐMKL.

16 Find mÐJMK and mÐLMK.

Algebra Find the values of the indicated variables and measures.

18. x, mÐUWV, mÐUWT

17. x, IK

19. Construction. Trace triangle ABC exactly onto a piece of patty paper. Doing what you know how to do, create a circumscribed circle.

Name the point of concurrency of the angle bisectors.

20. 21.

22. Construction Trace triangle XYZ exactly onto a piece of patty paper, then, doing what you do, create an inscribed circle.

23. Is a median, an altitude, or neither? Explain.

Name each segment.

24. a median in ∆STU 25. an altitude in ∆STU

26. a median in ∆SBU ` 27. an altitude in ∆CBU

List the angles of each triangle in order from smallest to largest.

28. 29.

List the sides of each triangle in order from shortest to longest.

30.

31. Algebra List the sides in order from shortest to longest in ∆XYZ, with
mÐX = 50, mÐY = 5x + 10, and mÐZ = 5x.

Can a triangle have sides with the given lengths? Explain.

32. 10 in., 13 in., 18 in.

33. 6 m, 5 m, 12 m

The lengths of two sides of a triangle are given. Find the range of possible lengths for the third side.

43. 4, 8

35. 13, 8

1 / ______/ incenter / A. / A circle created by using the circumcenter. The circle is tangent to each vertex of a triangle.
2 / ______/ inscribed / B. / The point of concurrency in a triangle where the altitudes meet.
3 / ______/ circumcenter / C. / A segment inside a triangle that connects the midpoints of two sides.
4 / ______/ circumscribed / D. / A segment in a triangle that touches the vertex and bisects the opposite side.
5 / ______/ centroid / E. / A segment that cuts an angle in half.
6 / ______/ orthocenter / F. / An adjective that means 'at the same time'.
7 / ______/ altitude / G. / A segment in a triangle that touches the vertex and is perpendicular with the opposite side.
8 / ______/ median / H. / The point of concurrency in a triangle where the angle bisectors meet.
9 / ______/ perpendicular bisector / I. / The point of concurrency in a triangle where the perpendicular bisectors meet.
10 / ______/ midsegment / J. / The point of concurrency in a triangle where the medians meet. This point is the center of gravity in a triangle.
11 / ______/ angle bisector / K. / A segment in a triangle that doesn't have to touch a vertex. It creates a 90◦ angle with a side while it cuts it in half.
12 / ______/ concurrent / L. / A circle created by using the incenter. The circle is tangent to each side of a triangle.